Answer:
A=1, B=-1, C=-7, D=15
Explanation:
Off the top of my head, i can't remember the name of the rule, but if a function has a root of (a+bi), then it must also have a root of (a-bi).
You have a cubic polynomial, so it must have 3 roots. 2 roots are already given to you. Using the rule above, you can find the 3rd root, which would be (2-i).
So we have -3, (2+i), and (2-i). You can construct the equation by adding x to the additive inverse of each, giving you (x-(-3)), (x-(2+i)), and (x-(2-i))
Simplify then multiply all roots together to get the expanded polynomial. the coefficients are your answer.
(x+3)(x-(2-i))(x-(2+i))
(x-3)(x^2-4x+5)
x^3-x^2-7x+15